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1. (4) Find the next four terms of the recursively-defined sequence:
for all integers
2. (7) Let be defined by the formula , for all integers . Prove by induction that this sequence is a solution to the recurrence relation , for all integers where a1 = 11.
3. (4) Express the following 4th degree polynomial in x recusively:
2x4 + 3x3 + x2 – x + 2
4. (4) A worker at a scrapbook sticker company is promised a bonus if her productivity increases as an Arithmetic Sequence (Progression) over a period of 5 days. That is, on day n she must produce an = a1 + (n – 1)d stickers. If a1 = 100 and d = 5 what is the total number of stickers she must produce over the period of 5 days to get the bonus?
5. (6) A worker at a scrapbook sticker company increases her productivity of stickers by 10% every day for a period of days. If she produced 100 stickers in the first day how many stickers did she produce on her third day?
How would you express her pattern of productivity as a sequence of the form an = ?; where an is the number of stickers produced on day n.
6. (7) Which of the following are second-order linear homogeneous recurrence relations with constant coefficients? Place “yes” against all that are. If anyone is not give a reason.
7. (9) Find a closed form expression that is a solution to the sequence defined by the following recurrence relation and initial conditions (use the method of characteristic equation):
8. (9) Find a solution for the following recurrence relation and initial conditions (use the method of characteristic equation):
